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Orthogonal Procrustes Rotation Maximizing Congruence

Published online by Cambridge University Press:  01 January 2025

Frank B. Brokken
Frank B. Brokken*
Affiliation:
University of Groningen
*
Correspondence should be sent to Frank Brokken, Department of Education, University of Groningen, Westerhaven 16, k. 902, 9718 AW Groningen, The Netherlands.
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Abstract

Procedures for assessing the invariance of factors found in data sets using different subjects and the same variables are often using the least squares criterion, which appears to be too restrictive for comparing factors.

Tucker's coefficient of congruence, on the other hand, is more closely related to the human interpretation of factorial invariance than the least squares criterion. A method maximizing simultaneously the sum of coefficients of congruence between two matrices of factor loadings, using orthogonal rotation of one matrix is presented. As shown in examples, the sum of coefficients of congruence obtained using the presented rotation procedure is slightly higher than the sum of coefficients of congruence using Orthogonal Procrustes Rotation based on the least squares criterion.

Type
Original Paper
Information
Psychometrika , Volume 48 , Issue 3 , September 1983 , pp. 343 - 352
Copyright
Copyright © 1983 The Psychometric Society

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Footnotes

The author is obliged to Lewis R. Goldberg for critically reviewing the first draft of this paper.

References

Reference Note

Brokken, F. B. Orthogonal rotation to achieve congruence. Paper presented at the Spring meeting of the Psychometric Society, Chapel Hill, May 1981.Google Scholar

Reference

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